What is the Greatest Common Factor of 17764 and 17782?

Greatest common factor (GCF) of 17764 and 17782 is 2.

GCF(17764,17782) = 2

We will now calculate the prime factors of 17764 and 17782, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17764 and 17782.

How to find the GCF of 17764 and 17782?

We will first find the prime factorization of 17764 and 17782. After we will calculate the factors of 17764 and 17782 and find the biggest common factor number .

Step-1: Prime Factorization of 17764

Prime factors of 17764 are 2, 4441. Prime factorization of 17764 in exponential form is:

17764 = 2² × 4441¹

Step-2: Prime Factorization of 17782

Prime factors of 17782 are 2, 17, 523. Prime factorization of 17782 in exponential form is:

17782 = 2¹ × 17¹ × 523¹

Step-3: Factors of 17764

List of positive integer factors of 17764 that divides 17764 without a remainder.

1, 2, 4, 4441, 8882

Step-4: Factors of 17782

List of positive integer factors of 17782 that divides 17764 without a remainder.

1, 2, 17, 34, 523, 1046, 8891

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17764 and 17782. The biggest common factor number is the GCF number.
So the greatest common factor 17764 and 17782 is 2.

Also check out the Least Common Multiple of 17764 and 17782